Question: Multiply and simplify the following complex numbers: $({4+4i}) \cdot ({-2-5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({4+4i}) \cdot ({-2-5i}) = $ $ ({4} \cdot {-2}) + ({4} \cdot {-5i}) + ({4i} \cdot {-2}) + ({4i} \cdot {-5i}) $ Then simplify the terms: $ (-8) + (-20i) + (-8i) + (-20i^2) $ Imaginary unit multiples can be grouped together. $ -8 + (-20 - 8)i - 20 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -8 + (-20 - 8)i - (-20) $ The result is simplified: $ (-8 + 20) + (-28i) = 12-28i $